Learn Italian: Pensavo che il nonno non ci sentisse, ma ha sentito un bisbiglio. - I thought grandpa couldn't hear, but he heard a whisper.

This perfectly demonstrates the difference between sentirci and the regular verb sentire. We use the pronominal verb sentirci to talk about the physical capacity or ability to hear in general (in this case, thinking he was deaf or hard of hearing). However, we use the standard verb sentire when talking about perceiving a specific sound, like un bisbiglio (a whisper).

Why is sentisse in the subjunctive mood?

It follows the phrase Pensavo che (I thought that). Verbs expressing personal opinion, thought, or doubt generally require the subjunctive mood in the clause that follows them.

Why use the imperfect subjunctive (sentisse) in the first part, but the indicative (ha sentito) in the second?

The first action is governed by the past-tense trigger Pensavo che. Since the grandpa's hearing ability is a state happening at the same time as the thinking, we must use the imperfect subjunctive (sentisse). The second clause after ma (but) is an independent statement of fact—it's what actually happened, not influenced by what you thought—so it uses the normal indicative past tense (ha sentito).

Could I attach the ci to the end of the verb instead, like non sentisseci?